Usually when there is the form [time period] + 있으면, the implied meaning is "After [time period]" or "(With)in [time period]."
So, "사흘 있으면" means "In three days."
The full sentence translated means
"Because it will be a holiday in three days, the roads will be jammed."
The fuller form really is [time period] + 있으면 Noun + 이다, meaning "In [amount of time], it will be [Noun]."